Answer :
To solve this problem, we need to calculate the taxable equivalent yield for each investment using the given formula:
[tex]\[ \text{Taxable Equivalent Yield} = \frac{\text{Tax-Free Yield}}{1 - \frac{\text{Tax Bracket}}{100}} \][/tex]
Let's perform these calculations for each investment one by one.
1. For the tax bracket of 18% and a tax-free yield of 3%:
[tex]\[ \text{Taxable Equivalent Yield} = \frac{3\%}{1 - \frac{18}{100}} = \frac{3}{0.82} \approx 3.6585\% \][/tex]
2. For the tax bracket of 32% and a tax-free yield of 4%:
[tex]\[ \text{Taxable Equivalent Yield} = \frac{4\%}{1 - \frac{32}{100}} = \frac{4}{0.68} \approx 5.8824\% \][/tex]
3. For the tax bracket of 32% and a tax-free yield of 3%:
[tex]\[ \text{Taxable Equivalent Yield} = \frac{3\%}{1 - \frac{32}{100}} = \frac{3}{0.68} \approx 4.4118\% \][/tex]
4. For the tax bracket of 22% and a tax-free yield of 5%:
[tex]\[ \text{Taxable Equivalent Yield} = \frac{5\%}{1 - \frac{22}{100}} = \frac{5}{0.78} \approx 6.4103\% \][/tex]
5. For the tax bracket of 24% and a tax-free yield of 6%:
[tex]\[ \text{Taxable Equivalent Yield} = \frac{6\%}{1 - \frac{24}{100}} = \frac{6}{0.76} \approx 7.8947\% \][/tex]
Now, we need to order these yields from least to greatest.
The calculated yields are:
1. [tex]\(\approx 3.6585\%\)[/tex]
2. [tex]\(\approx 5.8824\%\)[/tex]
3. [tex]\(\approx 4.4118\%\)[/tex]
4. [tex]\(\approx 6.4103\%\)[/tex]
5. [tex]\(\approx 7.8947\%\)[/tex]
Arranging these in ascending order:
[tex]\[ \begin{array}{|l|c|} \hline & \text{Yield (\%)} \\ \hline 1. & 3.6585\% \\ 2. & 4.4118\% \\ 3. & 5.8824\% \\ 4. & 6.4103\% \\ 5. & 7.8947\% \\ \hline \end{array} \][/tex]
Therefore, the correct order of the investments from least to greatest return is:
[tex]\[\text{tax bracket: 18\% tax-free yield: 3\%}\][/tex]
[tex]\[< \text{tax bracket: 32\% tax-free yield: 3\%}\][/tex]
[tex]\[< \text{tax bracket: 32\% tax-free yield: 4\%}\][/tex]
[tex]\[< \text{tax bracket: 22\% tax-free yield: 5\%}\][/tex]
[tex]\[< \text{tax bracket: 24\% tax-free yield: 6\%}\][/tex]
So, you fill the boxes in the following order:
1. tax bracket 18%, tax-free yield 3%
2. tax bracket 32%, tax-free yield 3%
3. tax bracket 32%, tax-free yield 4%
4. tax bracket 22%, tax-free yield 5%
5. tax bracket 24%, tax-free yield 6%
[tex]\[ \text{Taxable Equivalent Yield} = \frac{\text{Tax-Free Yield}}{1 - \frac{\text{Tax Bracket}}{100}} \][/tex]
Let's perform these calculations for each investment one by one.
1. For the tax bracket of 18% and a tax-free yield of 3%:
[tex]\[ \text{Taxable Equivalent Yield} = \frac{3\%}{1 - \frac{18}{100}} = \frac{3}{0.82} \approx 3.6585\% \][/tex]
2. For the tax bracket of 32% and a tax-free yield of 4%:
[tex]\[ \text{Taxable Equivalent Yield} = \frac{4\%}{1 - \frac{32}{100}} = \frac{4}{0.68} \approx 5.8824\% \][/tex]
3. For the tax bracket of 32% and a tax-free yield of 3%:
[tex]\[ \text{Taxable Equivalent Yield} = \frac{3\%}{1 - \frac{32}{100}} = \frac{3}{0.68} \approx 4.4118\% \][/tex]
4. For the tax bracket of 22% and a tax-free yield of 5%:
[tex]\[ \text{Taxable Equivalent Yield} = \frac{5\%}{1 - \frac{22}{100}} = \frac{5}{0.78} \approx 6.4103\% \][/tex]
5. For the tax bracket of 24% and a tax-free yield of 6%:
[tex]\[ \text{Taxable Equivalent Yield} = \frac{6\%}{1 - \frac{24}{100}} = \frac{6}{0.76} \approx 7.8947\% \][/tex]
Now, we need to order these yields from least to greatest.
The calculated yields are:
1. [tex]\(\approx 3.6585\%\)[/tex]
2. [tex]\(\approx 5.8824\%\)[/tex]
3. [tex]\(\approx 4.4118\%\)[/tex]
4. [tex]\(\approx 6.4103\%\)[/tex]
5. [tex]\(\approx 7.8947\%\)[/tex]
Arranging these in ascending order:
[tex]\[ \begin{array}{|l|c|} \hline & \text{Yield (\%)} \\ \hline 1. & 3.6585\% \\ 2. & 4.4118\% \\ 3. & 5.8824\% \\ 4. & 6.4103\% \\ 5. & 7.8947\% \\ \hline \end{array} \][/tex]
Therefore, the correct order of the investments from least to greatest return is:
[tex]\[\text{tax bracket: 18\% tax-free yield: 3\%}\][/tex]
[tex]\[< \text{tax bracket: 32\% tax-free yield: 3\%}\][/tex]
[tex]\[< \text{tax bracket: 32\% tax-free yield: 4\%}\][/tex]
[tex]\[< \text{tax bracket: 22\% tax-free yield: 5\%}\][/tex]
[tex]\[< \text{tax bracket: 24\% tax-free yield: 6\%}\][/tex]
So, you fill the boxes in the following order:
1. tax bracket 18%, tax-free yield 3%
2. tax bracket 32%, tax-free yield 3%
3. tax bracket 32%, tax-free yield 4%
4. tax bracket 22%, tax-free yield 5%
5. tax bracket 24%, tax-free yield 6%
